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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Diameter of cylinder, d1		m
Length of cylinder, L		m
Modulus of elasticity of cylinder, E1		109N/m2
Poisson's ratio of cylinder, υ1
Modulus of elasticity of flat body, E2		109N/m2
Poisson's ratio of flat body, υ2
Force applied, F		N

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OUTPUT   VARIABLES   &   GRAPHS

VARIABLES	Values	Units
♦ Half width of contact area, b		10-6m	Graphs:  Stresses Vs Distance in z direction, Cylinder    Stresses Vs Distance in z direction, Flat body
♦ Max contact Pressure, pmax		106N/m2
♦ Normalized shear stress in cylinder, τmax,1		pmax
♦ τ max,1 acting at normalized distance		b
♦ Normalized shear stress in flat body, τmax,2		pmax
♦ τmax,2 acting at normalized distance		b

Stresses And Strains Due to Pressure Between Elastic Bodies

Contact loading occurs between machine elements such as rolling metal wheels, meshing gear teeth and bearings. Consider a cylinder on a flat body being subjected to a compressive force F. The initial point of contact develops into a rectangular area of contact (area = 2b*L) over which the load is distributed. The resulting stresses and deformation are described by the following equations:

where
     F = Compressive force
     z = direction of application of the force
     L = length of cylinder
     b = half width of contact area
     p_max = maximum contact pressure
     δ = displacement along axis of loading
     d₁ = diameter of cylinder
     E₁ = modulus of elasticity of cylinder
     υ₁ = Poisson's ratio of cylinder
     E₂ = modulus of elasticity of flat body
     υ₂ = Poisson's ratio of flat body
     υ = Poisson's ratio of body of interest
     σ_x = principal stress in x direction, for body of interest
     σ_y = principal stress in y direction
     σ_z = principal stress in z direction
     τ_max = maximum shear stress

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 3.
• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002, Chapter 14.
• Moulton A, Grosjean J & Owen G; The Moulton Formulae and Methods - directly usable for calculations in mechanical engineering; Professional Engineering Publishing Ltd, London, UK, 2005.